Large-Scale Constrained Optimization

9424639吉尔这项研究的目标是开发、研究和实现解决大规模非线性优化问题的算法。大规模优化问题具有变量多、约束条件多的特点。两种解决方案构成了本研究的重点。这两种方法分别是内点(障碍)法和序列二次规划(SQP)法。对内点的兴趣源于他们在线性规划问题上的成功，以及当遇到某些困难的约束时可能有价值的一些有趣的性质。内点法可以用来消除对矩阵特征值的约束。另一方面，由于解决中小型问题的方法的成功，以及调查员在两类性质截然不同的大型实际问题上使用这项技术的经验，促使人们对使用SQP产生兴趣。如果这些方法成功，开发的算法将被编码到软件中，以方便从业者应用。有几个工程、制造、科学和商业问题可以用大规模的非线性优化模型来描述。到目前为止，寻找一种类似于线性规划问题单纯形法的大规模优化问题的通用求解算法一直是优化界面临的一个挑战。如果成功，这项研究中正在研究的算法可能会打开更好地理解这类优化问题的窗口。人类努力的各个领域的许多问题都将从这项工作的结果中受益。

9424639 Gill The objective of this research is to develop, study, and implement algorithms for solving large-scale, nonlinear optimization problems. A large-scale optimization problem is characterized by a large number of variables and constraints. Two solution approaches form the focus of the research. These approaches are respectively, the interior point (barrier) method and the sequential quadratic programming (SQP) method. The interest in in the interior point stems from their success on linear programming problems, and some interesting properties that may be of value when certain difficult constraints are encountered. The interior point method can be used to eliminate constraints on the eigenvalues of a matrix. On the other hand, interest on the use of SQP is prompted by the success of the approach on small and medium-sized problems, and the experiences of the investigators on the performance of the technique on two classes of large, practical problems that differ substantially in character. If successful with these approaches, the developed algorithms will be coded into a software to facilitate their applications by practitioners. There are several engineering, manufacturing, scientific, and business problems that can be described by large-scale nonlinear optimization models. To date, finding a general solution algorithm to large scale optimization problems similar to the simplex method to linear programming problems has been a challenge to the optimization community. If successful, the algorithms being investigated in this research could open the window to a better understanding of this class of optimization problems. Many problems in various areas of human endeavor stand to benefit from the results of this work.